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Normal Distribution

The Normal distribution is one of the most commonly referred to distributions in statistical analysis and even in everyday conversations. A large body of academic and scholarly work rests on the fundamental assumption that the underlying data follows a Normal distribution that generates a bell-shaped curve. Mathematically, Normal distribution is expressed as shown in Equation 6.1:

Where x is a random variable, μ is the mean and σ is the standard deviation. The standard normal curve refers to 0 mean and constant variance; that is, σ = 1 and is represented mathematically as shown in Equation 6.2:

I generate a regular sequence of numbers (x) between –4 and 4. I can transform x as per Equation 6.2 into y. The plot in Figure 6.6 presents the standard normal curve or the probability density function, which plots the random variable x on the x-axis and density (y) on the y-axis.

Figure 6.6

Figure 6.6 The bell-shaped Normal distribution curve

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